Browse > Article
http://dx.doi.org/10.9722/JGTE.2014.24.1.17

A Case Study about Influence of Primary Mathematic Concepts on the Composition of Mathematic Concepts in 3rd grade Prodigies of Elementary Schools - Focusing on Addition and Multiplication of Fractions -  

Kim, Hwa Soo (Sehan University)
Publication Information
Journal of Gifted/Talented Education / v.24, no.1, 2014 , pp. 17-43 More about this Journal
Abstract
On the subjects of elementary 3rd grade three child prodigies who had learned the four fundamental arithmetic operations and primary concepts of fraction, this study conducted a qualitative case research to examine how they composed schema of addition and multiplication of fractions and transformed schema through recognition of precise concepts and linking of concepts with addition and multiplication of fractions as the contents. That is to say, this study investigates what schema and transformed schema child prodigies form through composition of primary mathematic concepts to succeed in relational understanding of addition and multiplication of fractions, how they use their own formed schema and transformed schema for themselves to approach solutions to problems with addition and multiplication of fractions, and how the subjects' concept formation and schema in their problem solving competence proceed to carry out transformations. As a result, we can tell that precise recognition of primary concepts, schema, and transformed schema work as crucial factors when addition of fractions is associated with multiplication of fractions, and then that the schema and transformed schema that result from the connection among primary mathematic concepts and the precise recognition of the primary concepts play more important roles than any other factors in creative problem solving with respect to addition and multiplication of fractions.
Keywords
Primary concepts; Secondary concepts; Schema; Transformed schema;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
연도 인용수 순위
1 고정일 외 백과사전 편찬부 (2003). 파스칼 세계대백과사전. 서울: 동서문화사.
2 고은성, 이경화, 송상헌 (2008). 수학영재 학생들의 정다면체 정의 구성 활동 분석. 영재교육연구, 18(1), 53-77.   과학기술학회마을
3 라병소 (1999). 수학 학습에서의 관계적 이해를 위한 스키마 구성에 관한 연구. 박사학위논문. 단국대학교.
4 방정숙, 정희진 (2006). 학습자중심 교수법에 대한 초등교사의 이해와 실행 형태: 수학적 의사소통을 중심으로. 학습자중심교과교육연구, 6(1), 297-321.
5 송상헌 (1998). 수학 영재성 측정과 판별에 관한 연구. 박사학위논문. 서울대학교.
6 오영열 (2002). 초등학교 교사들의 수업관행과 학생들의 학습환경 인식과의 관계. 학교수학, 4(2), 237-246.
7 Kuhs, T. M., & Ball, D. L. (1986). Approaches to teaching mathematics: Mapping the domains of Knowledge, Skills, and dispositions. Center on Teacher Education, Michigan State University.
8 Lampert, M. (1990). When the problem is not the question and the solution is not the answer: Mathematical knowing and teaching. American educational Research Journal, 27(1), 29-63.   DOI   ScienceOn
9 Ma, L. (1999). Knowing and teaching elementary mathematics teacher's understanding of fundamental mathematics in China and the United states. Hillsdale, NJ: Lawrence Erlbaum.
10 NCTM (2000). Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics, Inc.
11 National Research Council (1989). Everyday counts: A report to the nation on the future of mathematics education. Washington, DC: National Academy Press.
12 Raymond, A. M. (1997). Inconsistency between a begging elementary teacher' mathematics beliefs and teaching practice. Journal for Research in Mathematics Education, 28(5), 550-576.   DOI   ScienceOn
13 Reid, D. A. (2000). The Psychology of Student's Reasoning in School Mathematics: Grade2 Research Report. Acadia University Wolfville, Nova scotia, Canada.
14 Russell, S. J. (1999). Mathematical reasoning in the elementary grades. In L.V. Stiff, & F. R. Curcio (Eds.), Developing mathematical reasoning in grades K-12 (pp.22-36). Reston, VA: National Council of Teachers of Mathematics.
15 Sheffield, L. J. (1999). Developing Mathematically Promising Students. Reston, VA: National Council of Teachers of Mathematics.
16 이해영 (2005). 초등학교 5, 6학년 교사들의 수학적 의사소통 수업에 대한 인식과 교수실제. 석사학위논문. 한국교원대학교.
17 이종희, 김선희 (2002). 수학적 의사소통의 지도에 관한 실태조사. 학교수학, 4(1), 63-78.
18 Brown, S. I., Cooney, T. J., & Jones, D. (1990). Mathematics teacher education. In W. R. Houston (Ed.), Handbook of research on eacher education (pp. 639-656). New York: Macmillan.
19 이종희, 박선욱 (2002). 정보처리 양식에 따른 수학적 의사소통 능력과 문장제 해결능력과의 관계. 학교수학, 4(2), 147-160.   과학기술학회마을
20 황혜정, 나귀수, 최승현, 박경미, 임재훈, 서동엽 (2007). 수학교육학 신론. 서울: 문음사.
21 Curio, F. R. (1990). Mathematics as communication: Using a language-experience approach in the elementary grade. In T. Cooney, & C. R. Hirsch (Eds.), Teaching and learning mathematics in the 1990s. 1990 yearbook (pp. 69-75). Reston, VA: National Council of Teachers of Mathematics, Inc.
22 Fennema, E., Franke, M. L., Carpenter, T. P., & Carey, D. A. (1993). Using children's mathematical knowledge in education. American Educational Research Journal, 30(3), 555-583.   DOI
23 Johnson, D. T., & Sher, B. T. (1997). Resource Guide to Mathematics Curriculum Materials for High-ability Learners in Grades K-8. Williamsburg, VA: Centre for Gifted Education, College of William and Mary.
24 King, I. K. (1973). A Formative Development of an Elementary School Unit on Proof. Journal for Research in Mathematics Education, 4(1), 57-63.   DOI
25 NCTM (1991). Professional standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics, Inc.
26 동아출판사 (1985). 동아 新크라운 국어사전. 서울: 동아출판사.
27 Skemp, R. R. (1998). 수학학습심리학 [황우형 역]. 서울: 민음사. (원본출간년도: 1987).
28 Stein, M. K., & Brown, C. (1997). Teacher learning in a social context: Integrating collaborative and institutional processes with the study of teacher change. In E. Fennema, & B. S. Nelson (Eds.), Mathematics teachers in transition (pp. 155-192). Mahwah, NJ: Lawrence Erlbaum Associates.
29 Johnson, D. T. (1993). Mathematical Curriculum for the Gifted. In J. VanTassel-Baska (Ed.), Comprehensive Curriculum for Gifted Learners (pp. 231-261). Needham Heights, MA: Allyn and Bacon.